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Mixed Region Covariance Discriminative Learning for Image Classification on Riemannian Manifolds

机译：混合区协方差鉴定图像分类对黎曼歧管的判别学习

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摘要

Covariance matrices, known as symmetric positive definite (SPD) matrices, are usually regarded as points lying on Riemannian manifolds. We describe a new covariance descriptor, which could improve the discriminative learning ability of region covariance descriptor by taking into account the mean of feature vectors. Due to the specific geometry of Riemannian manifolds, classical learning methods cannot be directly used on it. In this paper, we propose a subspace projection framework for the classification task on Riemannian manifolds and give the mathematical derivation for it. It is different from the common technique used for Riemannian manifolds, which is to explicitly project the points from a Riemannian manifold onto Euclidean space based upon a linear hypothesis. Under the proposed framework, we define a Gaussian Radial Basis Function- (RBF-) based kernel with a Log-Euclidean Riemannian Metric (LERM) to embed a Riemannian manifold into a high-dimensional Reproducing Kernel Hilbert Space (RKHS) and then project it onto a subspace of the RKHS. Finally, a variant of Linear Discriminative Analyze (LDA) is recast onto the subspace. Experiments demonstrate the considerable effectiveness of the mixed region covariance descriptor and the proposed method.
机译：称为对称正定（SPD）矩阵的协方差矩阵通常被认为是躺在riemannian歧管上的点。我们描述了一种新的协方差描述符，可以通过考虑特征向量的平均值来改善区域协方差描述符的辨别能力。由于Riemannian歧管的特定几何形状，无法直接使用古典学习方法。在本文中，我们向Riemannian歧管上提出了一个用于分类任务的子空间投影框架，并为其提供数学推导。它与用于黎曼歧管的常用技术不同，这是基于线性假设将从riemannian歧管的点显式投射到欧几里德空间中。在拟议的框架下，我们定义了基于高斯径向基函数 - （RBF-）的内核，具有LOG-euclidean riemannian度量（LERM），以将Riemannian歧管嵌入到高维再现内核HILBERT空间（RKHS）中，然后将其投影在rkhs的子空间上。最后，线性鉴别分析（LDA）的变体在子空间中重新循环。实验证明了混合区域协方差描述符和所提出的方法的相当有效性。

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  • 来源
    《Mathematical Problems in Engineering》 |2019年第5期|1261398.1-1261398.11|共11页
  • 作者

    Liu Xi; Ma Zhengming; Niu Guo;

  • 作者单位

    Sun Yat Sen Univ Sch Elect & Informat Technol Guangzhou 510006 Guangdong Peoples R China;

    Sun Yat Sen Univ Sch Elect & Informat Technol Guangzhou 510006 Guangdong Peoples R China|Sun Yat Sen Univ Nanfang Coll Guangzhou 510275 Guangdong Peoples R China;

    Foshan Univ Sch Elect Informat Engn Foshan 528000 Peoples R China;

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